Question: Solve for $x$ and $y$ using elimination. ${6x-3y = -24}$ ${5x-3y = -25}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${6x-3y = -24}$ $-5x+3y = 25$ Add the top and bottom equations together. ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {6x-3y = -24}\thinspace$ to find $y$ ${6}{(1)}{ - 3y = -24}$ $6-3y = -24$ $6{-6} - 3y = -24{-6}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {5x-3y = -25}\thinspace$ and get the same answer for $y$ : ${5}{(1)}{ - 3y = -25}$ ${y = 10}$